The manuscript is structured as follows. First, we give a brief overview of those elements of the Smoluchowski theory [1]}, [2]}, [3]}, [4]} needed to explain the proposed algorithm. Then, to be specific, we consider a stochastic simulation algorithm that has been described before [5]} and that uses exact solutions to propagate a molecule pair. Next, we show how the same can be achieved much swifter but virtually equally accurate. Finally, we consider a few examples and construct, via the proposed simulation method, the PDF corresponding to a non-reactive, irreversible and reversible reacting pair in 3D and 2D, respectively.
